Hydrodynamic Fingering Instability Induced by a Precipitation Reaction

Abstract

We experimentally demonstrate that a precipitation reaction at the miscible interface between two reactive solutions can trigger a hydrodynamic instability due to the buildup of a locally adverse mobility gradient related to a decrease in permeability. The precipitate results from an A þ B → C type of reaction when a solution containing one of the reactants is injected into a solution of the other reactant in a porous medium or a Hele-Shaw cell. Fingerlike precipitation patterns are observed upon displacement, the properties of which depend on whether A displaces B or vice versa. A mathematical modeling of the underlying mobility profile confirms that the instability originates from a local decrease in mobility driven by the localized precipitation. Nonlinear simulations of the related reaction-diffusion-convection model reproduce the properties of the instability observed experimentally. In particular, the simulations suggest that differences in diffusivity between A and B may contribute to the asymmetric characteristics of the fingering precipitation patterns. DOI: 10.1103/PhysRevLett.113.024502 PACS numbers: 47.55.P−, 47.15.gp, 47.56.+r, 47.70.Fw Chemical reactions are able to influence and even more strikingly induce hydrodynamic fingering instabilities of a frontal interface when a high mobility fluid displaces a less mobile one in a porous medium. This occurs in viscous fingering if a less viscous fluid displaces a more viscous one [1]. Fingering can also result from a change in permeability in a porous medium as in reactive dissolution instabilities [2][3][4][5][6][7][8][9][10]. In these cases, the invading fluid contains chemicals which dissolve the solid matrix of the porous medium, leading to a related increase in porosity behind the reaction front. As a result, the resistance to flow decreases in these higher mobility reactive zones, which favors further dissolution, giving, thus, a positive feedback leading to instability. Dispersion of reactants is the stabilizing factor counteracting the growth of fluid channels in order to provide a fingered pattern with a given characteristic wavelength [2,5,7,10]. The reverse case of precipitation is not expected to destabilize an interface as the related decrease in permeability and, hence, in mobility behind the front is expected to block the flow rather than destabilize it. There is, however, increased interest to understand the effect of precipitation reactions during flow displacements in porous media in the context of CO 2 sequestration techniques [11][12][13][14]. Mineralization by which CO 2 injected in a porous medium could undergo precipitation reactions (to yield carbonates, for instance [13][14][15][16]) is indeed promising in view of a permanent safe storage of CO 2 in geological strata. Understanding the conditions in which precipitations can affect the stability of the spreading CO 2 plumes [12] is, thus, particularly important.In this context, we demonstrate experimentally and explain theoretically how a precipitation reaction localized at th...

Genericity of confined chemical garden patterns with regard to changes in the reactants

“…The focus should thus be put on physical phenomena to understand and model this selection and to forge a link between chemical garden precipitates and other patterns obtained in similar growth conditions with other reactions. [30][31][32] For example, the relative viscosity and density of the two solutions may control the observed structures in some regions of the phase diagram (flower pattern for instance). The cohesive strength of the agglomerate of precipitate, measured as the force per unit area it can sustain before rupture, compared to the fluid pressure should also be an important parameter to understand the various morphologies observed in our experiments.…”

“…In our case, this gap is filled with one of the solutions, and the other solution is injected radially at a constant flow rate, the reaction taking place in the contact zone between the two solutions. [29][30][31][32] Under such conditions, a large variety of reproducible precipitation patterns emerges. Fig.…”

Thermodynamic coarsening arrested by viscous fingering in partially miscible binary mixtures

“…On the other, the well-known viscous fingering hydrodynamic instability [16][17][18][19] induces phase branching, splitting, and pinch off [20][21][22]. While many aspects of viscous fingering have been studied-including its role on fluid mixing [23][24][25] and ensuing chemical reactions [26][27][28]-its impact on phase separation of a fluid mixture remains unexplored.…”

Complexity from precipitation reactions

“…Depending on the used reactant concentrations, the boundary between these two domains ranges from sharp and walllike to broad and diffuse. The latter structures are reminiscent of reactive displacement patterns first reported by Nagatsu et al (10), who studied the formation of KFe[Fe(CN) 6 ] (a blue precipitate) in Hele-Shaw cells. The sharp, solid walls can trace the shapes of logarithmic spirals over distance of several centimeters.…”